High-redshift cosmography with a possible cosmic distance duality relation violation

The Cosmic Distance Duality Relation (CDDR) defines a fundamental link in modern cosmology between geometric distance measurements and redshift. Any observed deviations from the CDDR could suggest the need for new physics beyond the ΛCDM model. In this study, we model geometric distances (both luminosity and angular) using a cosmographic expansion with the Pade method, which stabilizes the behavior of the cosmographic series at high redshifts. This approach allows us to determine geometric distances independently of any specific model. By incorporating updated data from supernovae (SN), baryon acoustic oscillations (BAO), and cosmic chronometers (CC), we obtain observational constraints for parametric models that quantify the CDDR, alongside all baseline cosmographic parameters. We find that potential CDDR violations introduce new statistical correlations in the cosmographic parameters (H₀, q₀, and j₀). However, within this framework, we do not observe significant deviations from the CDDR, and our results remain consistent with the predictions of the ΛCDM model. This work offers a novel and straightforward method for testing the CDDR by fixing background evolution through cosmographic techniques, thereby paving the way for new geometric observational tests of possible deviations from standard cosmology.